1. **Problem 1: Area of parallelogram B** We are given two parallelograms A and B with bases 4 cm and 6 cm respectively. The area of parallelogram A is 28 cm². We need to find the area of parallelogram B. 2. **Formula and rules:** The area of a parallelogram is given by: $$\text{Area} = \text{base} \times \text{height}$$ Since the parallelograms are similar, their heights are proportional to their bases. 3. **Step-by-step solution:** - Let the height of parallelogram A be $h_A$ and height of B be $h_B$. - Area of A: $$28 = 4 \times h_A \implies h_A = \frac{28}{4} = 7$$ - Since the parallelograms are similar, the ratio of heights equals the ratio of bases: $$\frac{h_B}{h_A} = \frac{6}{4} = \frac{3}{2}$$ - So, $$h_B = h_A \times \frac{3}{2} = 7 \times \frac{3}{2} = 10.5$$ - Area of B: $$\text{Area}_B = \text{base}_B \times h_B = 6 \times 10.5 = 63$$ --- 4. **Problem 2: Area of shape A** Two similar shapes A and B have heights 3 cm and 15 cm respectively. Area of shape B is 150 cm². Find the area of shape A. 5. **Formula and rules:** For similar shapes, areas scale as the square of the ratio of corresponding lengths. 6. **Step-by-step solution:** - Ratio of heights: $$\frac{3}{15} = \frac{1}{5}$$ - Ratio of areas: $$\left(\frac{1}{5}\right)^2 = \frac{1}{25}$$ - Area of A: $$\text{Area}_A = \text{Area}_B \times \frac{1}{25} = 150 \times \frac{1}{25} = 6$$ **Final answers:** - Area of parallelogram B = 63 cm² - Area of shape A = 6 cm²